試題分析:如圖,連結
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,由正方體的性質可知
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,所以
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或其補角為異面直線
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與
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所成的角,而
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為正三角形,所以
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,故異面直線
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與
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所成的角為
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.
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來源:不詳
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如圖,邊長為2的正方形ACDE所在的平面與平面ABC垂直,AD與CE的交點為M,
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,且AC=BC.
(1)求證:
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平面EBC;
(2)求二面角
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的大小.
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如圖,在空間直角坐標系O-xyz中,正四棱錐P-ABCD的側棱長與底邊長都為
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,點M,N分別在PA,BD上,且
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.
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(本小題滿分12分)在三棱柱
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中,側面
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為矩形,
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,
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,
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為
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的中點,
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與
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交于點
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,
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側面
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.
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(1)證明:
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;
(2)若
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,求直線
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與平面
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所成角的正弦值.
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在三棱錐
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中,

是邊長為2的正三角形,平面

平面
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,
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,
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分別為
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的中點.

(1)證明:

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
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若四棱柱

的底面是邊長為1的正方形,且側棱垂直于底面,若
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與底面
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成60°角,則二面角

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在二面角

中,
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且
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若
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,
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, 則二面角

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在三棱柱
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來源:不詳
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正三棱錐P—ABC中,CM=2PM,CN=2NB,對于以下結論:
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①二面角B—PA—C大小的取值范圍是(
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,π);
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;
③過點M與異面直線PA和BC都成

的直線有3條;
④若二面角B—PA—C大小為
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,則過點N與平面PAC和平面PAB都成
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的直線有3條.
正確的序號是
.
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